It marked Moyes' final home game in charge before his move to Manchester United.
"I am a football supporter and if I had been on the terraces today I would have clapped the manager - I might not have liked what he was doing but I would have certainly applauded," said the Scot, who was given a guard of honour by his own players prior to the post-match lap of appreciation and was visibly moved.
"I think just by the reaction from most people in the last few days I thought it would be okay but if you are a football supporter you are entitled to support your team and if someone is not on your team you don't know what will be the reaction.
"It was really emotional from the moment I came in: all the stewards were standing clapping me and I didn't know what to do.
"I came here 11 years ago and it was really emotional walking out on to the pitch, a lot of people didn't know who I was I don't think.
"I got off to a great start (winning 2-1 over Fulham) so I am really fortunate I had a reception like I did today.
"I am gobsmacked, very thankful and humble for what the people of Everton have shown today.
"What I will miss is what you saw in the middle of the second half - the supporters were not cheering David Moyes, they were cheering their football club and standing up for it.
"I thought that was the toughest part for me today - it was a difficult time - because the crowd showed how big Everton are and what it means to them."